The chain-level intersection product for PL pseudomanifolds revisited

Journal of Singularities
volume 17 (2018), 330-367

Received: 3 December 2018. Received in revised form: 5 September 2018.

DOI: 10.5427/jsing.2018.17n

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Abstract:

We generalize the PL intersection product for chains on PL manifolds and for intersection chains on PL stratified pseudomanifolds to products of locally finite chains on non-compact spaces that are natural with respect to restriction to open sets. This is necessary to sheafify the intersection product, an essential step in proving duality between the Goresky-MacPherson intersection homology product and the intersection cohomology cup product pairing recently defined by the author and McClure. We also provide a correction to the Goresky-MacPherson proof of a version of Poincaré duality on pseudomanifolds that is used in the construction of the intersection product.

Keywords:

PL chains, Borel-Moore chains, intersection pairing, pseudomanifold, intersection homology

Mathematical Subject Classification (2010):

Primary: 55N45, 55M05, 55N33 ; Secondary: 57N80, 57Q65

Author(s) information:

Greg Friedman
Texas Christian University
Fort Worth, TX 76129 USA
email: greg.b.friedman@gmail.com